论文标题
部分可观测时空混沌系统的无模型预测
Weak lensing of gravitational waves in wave optics: Beyond the Born approximation
论文作者
论文摘要
宇宙的物质不均匀性在重力上会影响重力波（GWS）的传播，从而导致镜头效应。特别是，已经研究了GWS的弱透镜在天生近似范围内，以限制小规模的功率谱。在这项工作中，通过考虑重力电势$φ$中的高阶项来研究出生近似的有效性。为此，我们制定了出生后的近似值，并在$φ$中得出了放大倍率$ k $和相位调制$ s $最高的第三订单。我们发现，$ s $和$ k $的平均值为非零，平均值$ s $取决于点质量的大小。由于这种尺寸依赖性，信号得到了增强，并且检测$ S $减少所需的GW事件数量。我们发现，在某些情况下，该数字可以与检测$ s $的差异所需的数字相提并论。此外，可以验证的是，对于黑暗低质量晕圈的镜头，出生后的校正比$ f \ geq0.01 $ 〜Hz的天生近似小几个数量级。但是，在存在点质量的情况下，存在一个条件，即诞生近似失败。我们将校正条款得出到诞生的近似值，并确定诞生近似不再存在的条件。对于放大倍数，只要GWS的波长大于Schwarzschild镜头半径，而对于相位调制，则天生的近似值是有效的。
The Universe's matter inhomogeneity gravitationally affects the propagation of gravitational waves (GWs), causing the lensing effect. Particularly, the weak lensing of GWs has been studied within the range of the Born approximation to constrain the small-scale power spectrum. In this work, the validity of the Born approximation is investigated by accounting for the higher-order terms in the gravitational potential $Φ$. To do so, we formulate the post-Born approximation and derive the magnification $K$ and the phase modulation $S$ up to third order in $Φ$. We find that the average of $S$ and $K$ is non-zero and that the average of $S$ depends on the size of the point mass. Due to this size dependency, the signal is enhanced, and the number of GW events required for detecting the average of $S$ decreases. We find that this number can become comparable to or even smaller than the number required for detecting the variance of $S$ in certain scenarios. In addition, it is verified that, for lensing by dark low-mass halos, the post-Born corrections are a few orders of magnitude smaller than the Born approximation at $f\geq0.01$~Hz. However, in the presence of the point mass, there is a condition under which the Born approximation fails. We derive the correction terms to the Born approximation and identify the condition under which the Born approximation no longer holds. For the magnification, the Born approximation is valid as long as the wavelength of GWs is larger than the Schwarzschild radius of lenses, while for the phase modulation, this condition is modified due to the physical size of the point mass.
